 Solution

ID: past-exam-of-the-chemistry-course-of-the-year-3-of-the-natural-sciences-course-of-the-university-of-cambridge/2022/paper-4/61/c/i/solution

r_{s}

is the radius of a sphere containing one electron at the local uniform density:

\frac{4}{3} π r_{s}^{3} ρ = 1, r_{s} = (\frac{3}{4 π ρ})^{1/3} .

In atomic units, the unpolarized homogeneous electron gas has exchange energy per electron

- 0.4582/ r_{s}

. The local density approximation applies that uniform-gas result at each position using the local density, then integrates the result weighted by

ρ

. It assumes local uniform-gas behavior rather than resolving nonlocal exchange explicitly.

 New to topics? Read the docs here!